In this section, we conduct a welfare analysis which quanties the utility losses resulting from limited participation in annuity markets. This welfare analysis is similar to the one in Cocco, Gomes, and Maenhout (2005) in which the authors compute utility losses generated by limited participation in equity markets. The substantial optimal fraction of annuities inside the households portfolio in most settings suggests that considerable utility gains can be reaped from optimally in- vesting in annuity markets in expectation. Surprisingly, we empirically observe a weak participation in annuity market in juxtaposition to the theoretical advantages of annuity purchases. Naturally, theories from behavioral nance might explain the annuity puzzle. One behavioral explanation might be that a household may not feel qualied enough to participate in annuity markets and shies away from real option decisions in order to avoid severe investment mistakes (see also Campbell (2006)). Another behavioral explanation could be that information costs related to annuity markets are considerably high from the perspective of the household. This issue has been addressed by Gomes and Michaelides (2005) among others in the context of the limited equity participation puzzle. However, modeling behavioral motives is beyond the scope of our analysis as we study the asset allocation problem with an- nuities. Hence, one part of the utility losses derived in our welfare analysis could be
Welfare Analysis: Equivalent Increase in Financial Wealth (Percentage Points) of Having Access to Annuity Markets
Age Case 60 70 80 90 Stylized case 14.41 16.00 23.75 49.83 With loads 9.54 12.79 16.51 31.16 With bequest 5.69 8.43 14.14 30.07 Males 5.35 8.95 18.75 41.31 Bad health 0.96 2.62 6.73 21.74 Low EIS (ψ= 0.1) 0.40 1.18 3.68 14.70 High EIS (ψ= 0.3) 8.34 11.87 21.30 43.80 Low RRA (ρ= 2) 0.00 0.00 0.42 0.10
Low pension income (ζ = 0.5) 6.87 8.75 14.18 30.19
High pension income (ζ = 1) 0.90 2.19 7.64 24.38
Table 3: This table reports welfare gains in the presence of annuity markets for all cases considered previously. The rst, stylized case assumes a female with maximum life-span age 20 - 100, no initial endowment, no administration costs for annuities, no mortality asymmetries, RRA = 5, EIS = 1/5, and a zero-bequest motive (k = 0). The second
case introduces administration costs for annuities δ = 0.073 and mortality asymmetries
(2000 Population Basic vs. 1996 U.S. Annuity 2000 Basic mortality table). The third case additionally considers a bequest motive (k= 2). The remaining cases are variations of the
third case with loads and bequest. Welfare gains are computed as the equivalent percentage increase in nancial wealth an individual without access to annuity markets would need in order to attain the same expected utility as in the case with annuity markets. The computations are done for age 60, 70, 80, and 90.
generated by behavioral problems. For all cases considered so far, we rst compute the expected utility of households living in a world with access to annuity markets. Then, we compute the expected utility of households having no access. Apparently, the expected utility will be always higher for individuals, since annuities expand the decision set. We numerically equate the expected utility of both cases for the age 60, 70, 80, and 90 respectively by raising the nancial wealth of households having no access to annuities. The dierence is called the equivalent increase in nancial wealth required to compensate the household for the lack of annuity markets. Table (3) shows that annuity markets imply a considerable rise in nancial wealth for the cases in which we derived high annuity fractions. In our stylized case, nancial wealth equivalently increases from 14.41 percent at age 60 up to 49.83 percent at age 90. Adding administrative costs and bequest subsequently, we observe an ap- parent decline of the equivalent increase in nancial wealth to 8.01 percent and to
20 30 40 50 60 70 80 90 100 0 1 2 3 4 5 6 7 8 Age Consumption Quantiles (10%,50%,90%)
Figure 5: Consumption Percentiles (10th, 50th, and 90th) with and without Annuities. The dashed (solid) lines reect the case with (without) annuities. The thick grey, thick black, and black lines reect the 90th, 50th, and 10th percentile, respectively. The calcu- lations are based on 100,000 Monte-Carlo simulations. We assume the case with bequest and loads.
5.69 percent at age 60. The discrepancy becomes considerably smaller for a higher age. The subsequent cases show an equivalent increase in nancial wealth of 30.12 percent and 30.07 percent at age 90, respectively.
Men will exhibit particularly high utility gains if they live longer than expected by the annuity mortality table. Bad health propositions imply smaller utility gains reecting the implicit costs of adverse mortality beliefs. The utility gain remains at low levels even for old individuals since they have purchased less annuities before. The higher the intertemporal elasticity of substitution, the higher is the utility gain from annuities because - as pointed out before - the individual is less concerned with short-term consumption smoothing and is more willing to bet on the mortality credit in the long-run. As expected, the lower the payments from the public pension systems and/or dened benet plans, the larger are the utility gains as well as the demand for annuities.
The equivalent increase in nancial wealth can be attributed to the mortality credit nancing extra consumption. To demonstrate the advantage in consumption possibilities we conduct a Monte Carlo analysis when computing the 10th, 50th, and 90th percentile of consumption for the cases including and excluding annuity
markets. gure (5) demonstrates that the distribution of consumption (10th, 50th, and 90th percentile) of a household with no annuity holdings is humped-shaped. In the case including annuity markets, the purchase of annuities nances extra con- sumption during retirement due to the return enhancing mortality credit.